What does bar represent in $\frac{1}{\tau}\int_0^\tau \frac{dG}{dt}\equiv\frac{\overline{dG}}{dt}$?

Question

What does bar represent on a differentiation? I had an equation like this

$$\frac{d}{dt}(\sum_i p_i\cdot r_i)=2T+\sum_i F_i \cdot r_i$$

Now they said to integrate it.

The time average of Eq. (3.24) over a time interval τ is obtained by integrating both sides with respect to t from 0 to τ , and dividing by τ :

Then I can see a bar on top of above equation.

$$\frac{1}{\tau}\int_0^\tau \frac{dG}{dt}\equiv\frac{\overline{dG}}{dt}=\overline{2T}+\overline{\sum_i F_i \cdot r_i}$$

Does the bar represent integration? I didn't ask why there's $\frac{1}{\tau}$ cause the book says they had divided by $\tau$ but my question is if we had divided by $\tau$ then why there's no $\tau$ in second and third term? (still I have the question)

Answer 1

Just as the AVERAGE of n numbers is the sum of the numbers divided by n so the AVERAGE of a function defined on the interval from a to b is the integral of the function from a to b divie by b- a.

That is what this is saying. As others have said, the over-line indicates the AVERAGE.